Wash the mint leaves and dry on paper towels.
In a medium saucepan, warm the milk, sugar, 1 cup (250 ml) heavy cream, salt, and fresh mint leaves. Do not boil.
Once the mixture is hot and steamy, remove from heat, cover, and let stand for an hour to infuse the mint flavor into the milk mixture.
Pour the milk mixture through a strainer to remove the mint leaves. If you like your ice cream really minty, press down on the mint leaves to extract any more flavor and color. Once the flavor is squeezed out, discard the mint. I don't do this as I like the mint flavor to be subtle.
Pour the remaining heavy cream into a large bowl and set the rinsed strainer over the top.
Rewarm the mint infused milk.
In a separate bowl, whisk together the egg yolks, then slowly pour some of the warm mint mixture into the yolks, whisking constantly, then add the warmed yolks back into the saucepan. Whisk.
Cook the custard, stirring constantly with a silicone spatula, until the mixture thickens and coats the spatula. If using an instant read thermometer, it should read around 170ºF.
Immediately strain the mixture into the cream in the large bowl, then stir the mixture over an ice bath until cool. This really helps cool the mixture down before refrigerating.
Refrigerate the mixture thoroughly, preferably overnight, then freeze it in your ice cream maker according to the manufacturer’s instructions. (I always chill it overnight). Place a storage container for the ice cream in the freezer. I use a glass loaf pan because It gets extra cold quickly.
While the mixture is freezing, melt the chocolate in a small bowl over a pot of simmering water, or in a microwave oven on low power, stirring until smooth.
When the ice cream in the machine is ready, scribble some of the chocolate into the chilled container, then add a layer of the just-churned ice cream to the container.
Scribble melted chocolate over the top of the ice cream, then quickly stir it in, breaking up the chocolate into irregular pieces. Continue layering the ice cream, scribbling more chocolate and stirring as you go.
When finished, cover and freeze until firm.